| Title:
|
Two-sided Tolerance Intervals in a Simple Linear Regression (English) |
| Author:
|
Chvosteková, Martina |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
52 |
| Issue:
|
2 |
| Year:
|
2013 |
| Pages:
|
31-41 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Numerical results for a simple linear regression indicate that the non-simultaneous two-sided tolerance intervals nearly satisfy the condition of multiple-use confidence intervals, see Lee and Mathew (2002), but the numerical computation of the limits of the multiple-use confidence intervals is needed. We modified the Lieberman–Miller method (1963) for computing the simultaneous two-sided tolerance intervals in a simple linear regression with independent normally distributed errors. The suggested tolerance intervals are the narrowest of all the known simultaneous two-sided tolerance intervals. The computation of the multiple-use confidence intervals based on the new simultaneous two-sided tolerance intervals is simple and fast. (English) |
| Keyword:
|
multiple-use confidence interval |
| Keyword:
|
simultaneous two-sided tolerance interval |
| MSC:
|
62F25 |
| MSC:
|
62J05 |
| idZBL:
|
Zbl 06296012 |
| idMR:
|
MR3202377 |
| . |
| Date available:
|
2013-12-18T15:20:48Z |
| Last updated:
|
2014-07-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143536 |
| . |
| Reference:
|
[1] Chvosteková, M.: Simultaneous two-sided tolerance intervals for a univariate linear regression model. Communications in Statistics, Theory and Methods 42 (2013), 1145–1152. MR 3031273, 10.1080/03610926.2012.724502 |
| Reference:
|
[2] Chvosteková, M.: Determination of two-sided tolerance interval in a linear regression model. Forum Statisticum Slovacum 6 (2010), 79–84. |
| Reference:
|
[3] Chvosteková, M., Witkovský, V.: Exact likelihood ratio test for the parameters of the linear regression model with normal errors. Measurement Science Review 9 (2009), 1–8. 10.2478/v10048-009-0003-9 |
| Reference:
|
[4] Krishnamoorthy, K., Mathew, T.: Statistical Tolerance Regions: Theory, Applications, and Computation. Wiley series in probability and statistics, Wiley, Chichester, 2009. MR 2500599 |
| Reference:
|
[5] Lee, Y., Mathew, T.: Advances on Theoretical and Methodological Aspects of Probability and Statistics. Taylor & Francis, London, 2002. MR 1987243 |
| Reference:
|
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| Reference:
|
[7] Lieberman, G. J., Miller, R. G., Hamilton, M. A.: Unlimited simultaneous discrimination intervals in regression. Biometrika 54 (1967), 133–145. MR 0217953, 10.1093/biomet/54.1-2.133 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| . |
